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Relational proofs for quantum programs

Authors:

Mingsheng Ying,

Li ZhouAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 4, Issue POPL

Article No.: 21, Pages 1 - 29

https://doi.org/10.1145/3371089

Published: 20 December 2019 Publication History

Abstract

Relational verification of quantum programs has many potential applications in quantum and post-quantum security and other domains. We propose a relational program logic for quantum programs. The interpretation of our logic is based on a quantum analogue of probabilistic couplings. We use our logic to verify non-trivial relational properties of quantum programs, including uniformity for samples generated by the quantum Bernoulli factory, reliability of quantum teleportation against noise (bit and phase flip), security of quantum one-time pad and equivalence of quantum walks.

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Cited By

Correnson AFinkbeiner B(2025)Coinductive Proofs for Temporal HyperlivenessProceedings of the ACM on Programming Languages10.1145/37048899:POPL(1568-1595)Online publication date: 7-Jan-2025
https://dl.acm.org/doi/10.1145/3704889
Xu YBarthe GZhou L(2025)Automating Equational Proofs in Dirac NotationProceedings of the ACM on Programming Languages10.1145/37048789:POPL(1227-1259)Online publication date: 7-Jan-2025
https://dl.acm.org/doi/10.1145/3704878
Avanzini MBarthe GDavoli DGrégoire B(2025)A Quantitative Probabilistic Relational Hoare LogicProceedings of the ACM on Programming Languages10.1145/37048769:POPL(1167-1195)Online publication date: 7-Jan-2025
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Index Terms

Relational proofs for quantum programs
1. Theory of computation

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 4, Issue POPL

January 2020

1984 pages

EISSN:2475-1421

DOI:10.1145/3377388

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Copyright © 2019 Owner/Author.

This work is licensed under a Creative Commons Attribution International 4.0 License.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 20 December 2019

Published in PACMPL Volume 4, Issue POPL

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Cited By

Correnson AFinkbeiner B(2025)Coinductive Proofs for Temporal HyperlivenessProceedings of the ACM on Programming Languages10.1145/37048899:POPL(1568-1595)Online publication date: 7-Jan-2025
https://dl.acm.org/doi/10.1145/3704889
Xu YBarthe GZhou L(2025)Automating Equational Proofs in Dirac NotationProceedings of the ACM on Programming Languages10.1145/37048789:POPL(1227-1259)Online publication date: 7-Jan-2025
https://dl.acm.org/doi/10.1145/3704878
Avanzini MBarthe GDavoli DGrégoire B(2025)A Quantitative Probabilistic Relational Hoare LogicProceedings of the ACM on Programming Languages10.1145/37048769:POPL(1167-1195)Online publication date: 7-Jan-2025
https://dl.acm.org/doi/10.1145/3704876
Piattini MHevia JPeterssen G(2024)Quantum Software Engineering: Practical ChallengesInternational Journal of Software Engineering and Knowledge Engineering10.1142/S021819402441002X34:09(1387-1413)Online publication date: 30-Aug-2024
https://doi.org/10.1142/S021819402441002X
Yu N(2024)Quantum temporal logic and reachability problems of matrix semigroupsInformation and Computation10.1016/j.ic.2024.105197300:COnline publication date: 1-Oct-2024
https://dl.acm.org/doi/10.1016/j.ic.2024.105197
(2024)ReferencesFoundations of Quantum Programming10.1016/B978-0-44-315942-8.00030-7(435-447)Online publication date: 2024
https://doi.org/10.1016/B978-0-44-315942-8.00030-7
Ying M(2024)Verification of quantum programsFoundations of Quantum Programming10.1016/B978-0-44-315942-8.00018-6(137-167)Online publication date: 2024
https://doi.org/10.1016/B978-0-44-315942-8.00018-6
Ying M(2024)Quantum Hoare logicFoundations of Quantum Programming10.1016/B978-0-44-315942-8.00016-2(91-134)Online publication date: 2024
https://doi.org/10.1016/B978-0-44-315942-8.00016-2
Ying M(2024)IntroductionFoundations of Quantum Programming10.1016/B978-0-44-315942-8.00009-5(1-9)Online publication date: 2024
https://doi.org/10.1016/B978-0-44-315942-8.00009-5
Yan PJiang HYu N(2024)Approximate Relational Reasoning for Quantum ProgramsComputer Aided Verification10.1007/978-3-031-65633-0_22(495-519)Online publication date: 24-Jul-2024
https://dl.acm.org/doi/10.1007/978-3-031-65633-0_22
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